Postural stability of constrained three dimensional robotic systems

A Lyapunov-based approach for the design of a PD controller for robotic systems that are subject to multiple constraints is developed. A candidate Lyapunov function is proposed for the proof of stability using the mechanical energy equation for constrained systems. Sufficient conditions for local and global stability of the unconstrained system are given. An analysis is presented for the unconstrained case and extended to the constrained case. To check the effectiveness of the proposed controller, an eight-link 3D biped model is considered. The system dynamic equations are first derived. Constraint support forces are later added to the system. Simulation of the model motion when equipped with the proposed controller shows that it exhibits a stable response in the unconstrained case.<>